upmanship

/ˈʌpmənʃɪp/
noun
  1. The skill or practice of gaining an advantage over others, especially by outdoing them in a clever or competitive way.
    • Their constant one-upmanship over who had the better vacation got tiresome.
    • His upmanship in the debate made him look more knowledgeable than his opponent.
    • In the office, there was a lot of upmanship as everyone tried to impress the boss.